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// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/math/log1pf.c
// https://git.musl-libc.org/cgit/musl/tree/src/math/log1p.c
const std = @import("../std.zig");
const math = std.math;
const expect = std.testing.expect;
/// Returns the natural logarithm of 1 + x with greater accuracy when x is near zero.
///
/// Special Cases:
/// - log1p(+inf) = +inf
/// - log1p(+-0) = +-0
/// - log1p(-1) = -inf
/// - log1p(x) = nan if x < -1
/// - log1p(nan) = nan
pub fn log1p(x: anytype) @TypeOf(x) {
const T = @TypeOf(x);
return switch (T) {
f32 => log1p_32(x),
f64 => log1p_64(x),
else => @compileError("log1p not implemented for " ++ @typeName(T)),
};
}
fn log1p_32(x: f32) f32 {
const ln2_hi = 6.9313812256e-01;
const ln2_lo = 9.0580006145e-06;
const Lg1: f32 = 0xaaaaaa.0p-24;
const Lg2: f32 = 0xccce13.0p-25;
const Lg3: f32 = 0x91e9ee.0p-25;
const Lg4: f32 = 0xf89e26.0p-26;
const u = @bitCast(u32, x);
var ix = u;
var k: i32 = 1;
var f: f32 = undefined;
var c: f32 = undefined;
// 1 + x < sqrt(2)+
if (ix < 0x3ED413D0 or ix >> 31 != 0) {
// x <= -1.0
if (ix >= 0xBF800000) {
// log1p(-1) = -inf
if (x == -1.0) {
return -math.inf(f32);
}
// log1p(x < -1) = nan
else {
return math.nan(f32);
}
}
// |x| < 2^(-24)
if ((ix << 1) < (0x33800000 << 1)) {
// underflow if subnormal
if (ix & 0x7F800000 == 0) {
math.doNotOptimizeAway(x * x);
}
return x;
}
// sqrt(2) / 2- <= 1 + x < sqrt(2)+
if (ix <= 0xBE95F619) {
k = 0;
c = 0;
f = x;
}
} else if (ix >= 0x7F800000) {
return x;
}
if (k != 0) {
const uf = 1 + x;
var iu = @bitCast(u32, uf);
iu += 0x3F800000 - 0x3F3504F3;
k = @intCast(i32, iu >> 23) - 0x7F;
// correction to avoid underflow in c / u
if (k < 25) {
c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
c /= uf;
} else {
c = 0;
}
// u into [sqrt(2)/2, sqrt(2)]
iu = (iu & 0x007FFFFF) + 0x3F3504F3;
f = @bitCast(f32, iu) - 1;
}
const s = f / (2.0 + f);
const z = s * s;
const w = z * z;
const t1 = w * (Lg2 + w * Lg4);
const t2 = z * (Lg1 + w * Lg3);
const R = t2 + t1;
const hfsq = 0.5 * f * f;
const dk = @intToFloat(f32, k);
return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
}
fn log1p_64(x: f64) f64 {
const ln2_hi: f64 = 6.93147180369123816490e-01;
const ln2_lo: f64 = 1.90821492927058770002e-10;
const Lg1: f64 = 6.666666666666735130e-01;
const Lg2: f64 = 3.999999999940941908e-01;
const Lg3: f64 = 2.857142874366239149e-01;
const Lg4: f64 = 2.222219843214978396e-01;
const Lg5: f64 = 1.818357216161805012e-01;
const Lg6: f64 = 1.531383769920937332e-01;
const Lg7: f64 = 1.479819860511658591e-01;
var ix = @bitCast(u64, x);
var hx = @intCast(u32, ix >> 32);
var k: i32 = 1;
var c: f64 = undefined;
var f: f64 = undefined;
// 1 + x < sqrt(2)
if (hx < 0x3FDA827A or hx >> 31 != 0) {
// x <= -1.0
if (hx >= 0xBFF00000) {
// log1p(-1) = -inf
if (x == -1.0) {
return -math.inf(f64);
}
// log1p(x < -1) = nan
else {
return math.nan(f64);
}
}
// |x| < 2^(-53)
if ((hx << 1) < (0x3CA00000 << 1)) {
if ((hx & 0x7FF00000) == 0) {
math.raiseUnderflow();
}
return x;
}
// sqrt(2) / 2- <= 1 + x < sqrt(2)+
if (hx <= 0xBFD2BEC4) {
k = 0;
c = 0;
f = x;
}
} else if (hx >= 0x7FF00000) {
return x;
}
if (k != 0) {
const uf = 1 + x;
const hu = @bitCast(u64, uf);
var iu = @intCast(u32, hu >> 32);
iu += 0x3FF00000 - 0x3FE6A09E;
k = @intCast(i32, iu >> 20) - 0x3FF;
// correction to avoid underflow in c / u
if (k < 54) {
c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
c /= uf;
} else {
c = 0;
}
// u into [sqrt(2)/2, sqrt(2)]
iu = (iu & 0x000FFFFF) + 0x3FE6A09E;
const iq = (@as(u64, iu) << 32) | (hu & 0xFFFFFFFF);
f = @bitCast(f64, iq) - 1;
}
const hfsq = 0.5 * f * f;
const s = f / (2.0 + f);
const z = s * s;
const w = z * z;
const t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
const R = t2 + t1;
const dk = @intToFloat(f64, k);
return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
}
test "math.log1p" {
try expect(log1p(@as(f32, 0.0)) == log1p_32(0.0));
try expect(log1p(@as(f64, 0.0)) == log1p_64(0.0));
}
test "math.log1p_32" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f32, log1p_32(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(0.2), 0.182322, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(0.8923), 0.637793, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(1.5), 0.916291, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(37.45), 3.649359, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(89.123), 4.501175, epsilon));
try expect(math.approxEqAbs(f32, log1p_32(123123.234375), 11.720949, epsilon));
}
test "math.log1p_64" {
const epsilon = 0.000001;
try expect(math.approxEqAbs(f64, log1p_64(0.0), 0.0, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(0.2), 0.182322, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(0.8923), 0.637793, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(1.5), 0.916291, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(37.45), 3.649359, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(89.123), 4.501175, epsilon));
try expect(math.approxEqAbs(f64, log1p_64(123123.234375), 11.720949, epsilon));
}
test "math.log1p_32.special" {
try expect(math.isPositiveInf(log1p_32(math.inf(f32))));
try expect(log1p_32(0.0) == 0.0);
try expect(log1p_32(-0.0) == -0.0);
try expect(math.isNegativeInf(log1p_32(-1.0)));
try expect(math.isNan(log1p_32(-2.0)));
try expect(math.isNan(log1p_32(math.nan(f32))));
}
test "math.log1p_64.special" {
try expect(math.isPositiveInf(log1p_64(math.inf(f64))));
try expect(log1p_64(0.0) == 0.0);
try expect(log1p_64(-0.0) == -0.0);
try expect(math.isNegativeInf(log1p_64(-1.0)));
try expect(math.isNan(log1p_64(-2.0)));
try expect(math.isNan(log1p_64(math.nan(f64))));
}
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